The basic equation for continuous compounding is as follows:
\(A=Pe^{rt}\)
Plugging in the given values gives:
\(10000=5000e^{0.027t}\)
Dividing both sides by 5000, we get:
\(2=e^{0.027t}\)
Take natural logs of each side:
\(ln\ 2=0.027t\)
from which we find that t = 25.67 years.
